21 citations · 60 across the 11 of their papers we have counts for
14 papers
Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field
Levent Alpöge, Manjul Bhargava, Wei Ho +1
We show that for any quadratic extension of number fields , there exists an abelian variety of positive rank whose rank does not grow upon base change to . This resul…
Quadratic enrichment of the logarithmic derivative of the zeta function
Margaret Bilu, Wei Ho, Padmavathi Srinivasan +2
We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. We…
On average sizes of Selmer groups and ranks in families of elliptic curves having marked points
Manjul Bhargava, Wei Ho
We determine average sizes/bounds for the - and -Selmer groups in various families of elliptic curves with marked points, thus confirming several cases of the Poonen--Rains h…
Everywhere local solubility for hypersurfaces in products of projective spaces
Tom Fisher, Wei Ho, Jennifer Park
We prove that a positive proportion of hypersurfaces in products of projective spaces over are everywhere locally soluble, for almost all multidegrees and dimensions,…
The second moment of the number of integral points on elliptic curves is bounded
Levent Alpöge, Wei Ho
Let be a number field and a finite set of places of containing all archimedean places. In this paper, we show that the second moment of the number of -integral point…
Galois closures of non-commutative rings and an application to Hermitian representations
Wei Ho, Matthew Satriano
Galois closures of commutative rank n ring extensions were introduced by Bhargava and the second author. In this paper, we generalize the construction to the case of non-commutativ…
Splitting Brauer classes using the universal Albanese
Wei Ho, Max Lieblich
We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese var…
Odd degree number fields with odd class number
Wei Ho, Arul Shankar, Ila Varma
For every odd integer , we prove that there exist infinitely many number fields of degree and associated Galois group whose class number is odd. To do so, we st…
Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks
Jennifer S. Balakrishnan, Wei Ho, Nathan Kaplan +3
Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes…
Zeta functions of a class of Artin-Schreier curves with many automorphisms
Irene Bouw, Wei Ho, Beth Malmskog +3
This paper describes a class of Artin-Schreier curves, generalizing results of Van der Geer and Van der Vlugt to odd characteristic. The automorphism group of these curves contains…
Orbit Parametrizations for K3 Surfaces
Manjul Bhargava, Wei Ho, Abhinav Kumar
We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characterist…
Coregular spaces and genus one curves
Manjul Bhargava, Wei Ho
A coregular space is a representation of an algebraic group for which the ring of polynomial invariants is free. In this paper, we show that the orbits of many coregular irreducibl…
Genus one curves and Brauer-Severi varieties
Aise Johan de Jong, Wei Ho
Let K be a field. Let A be a central simple algebra over K and let X be the associated Brauer-Severi variety over K. It has recently been asked if there exists a genus 1 curve C ov…
Moduli of products of stable varieties
Bhargav Bhatt, Wei Ho, Zsolt Patakfalvi +1
We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gi…